Focused GRE Quantitative Reasoning practice exam. This resource contains 180 questions covering algebra,
arithmetic, geometry, data interpretation, word problems, and quantitative comparison. Each question is
styled after the actual GRE, including multiple-choice and quantitative comparison formats. Every answer
includes a short rationale. Use this exam to strengthen your math skills and boost your GRE score.
Key Topics Covered
• Arithmetic – Integers, fractions, decimals, percentages, ratios, exponents, roots, absolute value, number
properties
• Algebra – Linear equations, inequalities, functions, quadratics, factoring, word problems, coordinate
geometry
• Geometry – Lines, angles, triangles, circles, quadrilaterals, area, perimeter, volume, coordinate geometry
• Data Interpretation – Descriptive statistics (mean, median, mode, range, standard deviation), probability,
counting methods, interpreting tables and graphs
• Quantitative Comparison – Comparing two quantities using algebraic, geometric, and numeric reasoning
• Word Problems – Rate, work, mixture, interest, age, distance, consecutive integer problems
Questions 1–180
1. If 4x + 7 = 31, what is the value of x?
A) 4
B) 6
C) 8
D) 10
Answer B: 6
Rationale: 4x = 24 → x = 6. Simple linear equation.
2. What is 35% of 200?
A) 50
B) 70
,C) 80
D) 100
Answer B: 70
Rationale: 0.35 × 200 = 70.
3. Quantity A: The slope of the line y = 3x – 2. Quantity B: The slope of the line 2y = 6x + 4.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined.
Answer C: The two quantities are equal.
Rationale: Both equations simplify to slope 3. B: 2y=6x+4 → y=3x+2, slope 3.
4. A rectangle has length 10 and width 6. What is its perimeter?
A) 16
B) 32
C) 60
D) 30
Answer B: 32
Rationale: Perimeter = 2(10+6)=2×16=32.
5. The average (arithmetic mean) of 12, 18, and x is 16. What is x?
A) 14
B) 18
C) 20
D) 22
Answer B: 18
Rationale: (12+18+x)/3=16 → 30+x=48 → x=18.
6. Which of the following is equivalent to 4² × 4³?
A) 4⁵
B) 4⁵
,C) 4⁶
D) 16⁶
Answer A: 4⁵
Rationale: Add exponents: 4²⁺³ = 4⁵.
7. A bag contains 6 red, 4 blue, and 5 green marbles. If one marble is drawn at random, what is the
probability it is not blue?
A) 4/15
B) 11/15
C) 2/5
D) 3/5
Answer B: 11/15
Rationale: Total = 15. Not blue = 6+5=11. Probability = 11/15.
8. Solve for x: 3(x – 4) = 2x + 5
A) 7
B) 17
C) 12
D) 10
Answer B: 17
Rationale: 3x-12=2x+5 → x=17.
9. The area of a circle is 36π. What is its radius?
A) 3
B) 6
C) 9
D) 12
Answer B: 6
Rationale: πr² = 36π → r²=36 → r=6.
10. If the ratio of boys to girls in a class is 3:5 and there are 15 boys, how many students are there?
A) 25
, B) 40
C) 30
D) 35
Answer B: 40
Rationale: Boys = 3 parts = 15 → 1 part=5. Girls = 5 parts=25. Total=40.
11. Quantity A: (0.75)². Quantity B: 0.75.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined.
Answer B: Quantity B is greater.
Rationale: 0.75² = 0.5625, which is less than 0.75. So B > A.
12. A car travels 150 miles in 3 hours. What is its average speed in miles per hour?
A) 45
B) 50
C) 55
D) 60
Answer B: 50
Rationale: Speed = distance/time = 150/3 = 50 mph.
13. If 2x + 3y = 12 and x = 3, then y = ?
A) 1
B) 2
C) 3
D) 4
Answer B: 2
Rationale: 2(3)+3y=12 → 6+3y=12 → 3y=6 → y=2.
14. What is the median of the set {5, 9, 3, 11, 7}?
A) 5
arithmetic, geometry, data interpretation, word problems, and quantitative comparison. Each question is
styled after the actual GRE, including multiple-choice and quantitative comparison formats. Every answer
includes a short rationale. Use this exam to strengthen your math skills and boost your GRE score.
Key Topics Covered
• Arithmetic – Integers, fractions, decimals, percentages, ratios, exponents, roots, absolute value, number
properties
• Algebra – Linear equations, inequalities, functions, quadratics, factoring, word problems, coordinate
geometry
• Geometry – Lines, angles, triangles, circles, quadrilaterals, area, perimeter, volume, coordinate geometry
• Data Interpretation – Descriptive statistics (mean, median, mode, range, standard deviation), probability,
counting methods, interpreting tables and graphs
• Quantitative Comparison – Comparing two quantities using algebraic, geometric, and numeric reasoning
• Word Problems – Rate, work, mixture, interest, age, distance, consecutive integer problems
Questions 1–180
1. If 4x + 7 = 31, what is the value of x?
A) 4
B) 6
C) 8
D) 10
Answer B: 6
Rationale: 4x = 24 → x = 6. Simple linear equation.
2. What is 35% of 200?
A) 50
B) 70
,C) 80
D) 100
Answer B: 70
Rationale: 0.35 × 200 = 70.
3. Quantity A: The slope of the line y = 3x – 2. Quantity B: The slope of the line 2y = 6x + 4.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined.
Answer C: The two quantities are equal.
Rationale: Both equations simplify to slope 3. B: 2y=6x+4 → y=3x+2, slope 3.
4. A rectangle has length 10 and width 6. What is its perimeter?
A) 16
B) 32
C) 60
D) 30
Answer B: 32
Rationale: Perimeter = 2(10+6)=2×16=32.
5. The average (arithmetic mean) of 12, 18, and x is 16. What is x?
A) 14
B) 18
C) 20
D) 22
Answer B: 18
Rationale: (12+18+x)/3=16 → 30+x=48 → x=18.
6. Which of the following is equivalent to 4² × 4³?
A) 4⁵
B) 4⁵
,C) 4⁶
D) 16⁶
Answer A: 4⁵
Rationale: Add exponents: 4²⁺³ = 4⁵.
7. A bag contains 6 red, 4 blue, and 5 green marbles. If one marble is drawn at random, what is the
probability it is not blue?
A) 4/15
B) 11/15
C) 2/5
D) 3/5
Answer B: 11/15
Rationale: Total = 15. Not blue = 6+5=11. Probability = 11/15.
8. Solve for x: 3(x – 4) = 2x + 5
A) 7
B) 17
C) 12
D) 10
Answer B: 17
Rationale: 3x-12=2x+5 → x=17.
9. The area of a circle is 36π. What is its radius?
A) 3
B) 6
C) 9
D) 12
Answer B: 6
Rationale: πr² = 36π → r²=36 → r=6.
10. If the ratio of boys to girls in a class is 3:5 and there are 15 boys, how many students are there?
A) 25
, B) 40
C) 30
D) 35
Answer B: 40
Rationale: Boys = 3 parts = 15 → 1 part=5. Girls = 5 parts=25. Total=40.
11. Quantity A: (0.75)². Quantity B: 0.75.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined.
Answer B: Quantity B is greater.
Rationale: 0.75² = 0.5625, which is less than 0.75. So B > A.
12. A car travels 150 miles in 3 hours. What is its average speed in miles per hour?
A) 45
B) 50
C) 55
D) 60
Answer B: 50
Rationale: Speed = distance/time = 150/3 = 50 mph.
13. If 2x + 3y = 12 and x = 3, then y = ?
A) 1
B) 2
C) 3
D) 4
Answer B: 2
Rationale: 2(3)+3y=12 → 6+3y=12 → 3y=6 → y=2.
14. What is the median of the set {5, 9, 3, 11, 7}?
A) 5
